MathDB

10.4

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 10.4 2n incenters collinear

Source:

6/7/2020
Let A1A2A3...AnA_1A_2A_3...A_n be a bicentric polygon with nn sides. Denote by IiI_i the incenter of triangle Ai−1AiAi+1,Ai(i+1)A_{i-1}A_iA_{i+1}, A_{i(i+1)} the intersection of AiAi+2A_iA_{i+2} and Ai−1Ai+1,Ii(i+1)A_{i-1}A_{i+1},I_{i(i+1)} is the incenter of triangle AiAi(i+1)Ai+1A_iA_{i(i+1)}A_{i+1} (i=1,ni = 1, n). Prove that there exist 2n2n points I1,I2,...,In,I12,I23,....,In1I_1, I_2, ..., I_n, I_{12}, I_{23}, ...., I_{n1} on the same circle.
Nguyễn Văn Linh
geometryincenterbicentric